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Publisher: Cambridge University Press   (Total: 372 journals)

 Compositio MathematicaJournal Prestige (SJR): 3.139 Citation Impact (citeScore): 1Number of Followers: 1      Subscription journal ISSN (Print) 0010-437X - ISSN (Online) 1570-5846 Published by Cambridge University Press  [372 journals]
• Galois theory for general systems of polynomial equations
• Authors: A. Esterov
Pages: 229 - 245
Abstract: We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois theory of general systems of polynomial equations, because arbitrary systems split into reduced irreducible ones upon monomial changes of variables. In particular, our result proves the multivariate version of the Abel–Ruffini theorem: the classification of general systems of equations solvable by radicals reduces to the classification of lattice polytopes of mixed volume 4 (which we prove to be finite in every dimension). We also notice that the monodromy of every general system of equations is either symmetric or imprimitive. The proof is based on a new result of independent importance regarding dual defectiveness of systems of equations: the discriminant of a reduced irreducible square system of general polynomial equations is a hypersurface unless the system is linear up to a monomial change of variables.
PubDate: 2019-02-01T00:00:00.000Z
DOI: 10.1112/S0010437X18007868
Issue No: Vol. 155, No. 2 (2019)

• Profinite detection of 3-manifold decompositions
• Authors: Henry Wilton; Pavel Zalesskii
Pages: 246 - 259
Abstract: The profinite completion of the fundamental group of a closed, orientable $3$ -manifold determines the Kneser–Milnor decomposition. If $M$ is irreducible, then the profinite completion determines the Jaco–Shalen–Johannson decomposition of $M$ .
PubDate: 2019-02-01T00:00:00.000Z
DOI: 10.1112/S0010437X1800787X
Issue No: Vol. 155, No. 2 (2019)

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